Resolving core-envelope degeneracies in giant planets and sub-Neptunes: Constraining the equivalence in the presence of dilute gradients

The widespread recognition of dilute, `fuzzy' cores in giant planets and massive volatile mantles in sub-Neptunes has transformed planetary interior modelling into a highly degenerate, multi-dimensional problem. To map the structural degeneracies introduced by these complex interiors, we present , an open-source static structural integrator with a unified layered architecture spanning rock-water-envelope sub-Neptunes through volatile-rich gas giants. The framework supports dense parameter sweeps over compositional gradients at fixed observed $(M_ , R_ , Z_ )$, enabling consistent forward-model exploration of interior degeneracies across the radius valley and the warm-giant population. fuzzycore p p atm The framework solves the equations of hydrostatic equilibrium across phase-separated iron, rock, and water layers beneath a gaseous envelope. We employed a highly resolved adaptive grid to model arbitrary heavy-element gradients within the envelope, parameterising the dilution width to systematically evaluate the structural impact of varying core-envelope boundaries. We benchmarked against an evolution-derived Jupiter profile, demonstrating that when envelope boundary metallicities and integrated heavy-element budgets are matched, the macroscopic planetary radius is robust to the exact functional topology of the gradient to within 2.3%. This empirical robustness allowed us to use smooth parameterisations to densely map interior degeneracies. Applying this to the sub-Neptune regime, we generated a water-world degeneracy atlas, quantifying how the required envelope metallicity and dilution width trade off against assumed water-mass fractions to reproduce a fixed planetary radius. fuzzycore By decoupling structural profiling from time-dependent energy transport and convective mixing, enables the systematic mapping of static degeneracies across the sub-Neptune and warm-giant populations at resolutions that complement, rather than replace, fully evolutionary Henyey treatments. It serves as a forward-model backend for linking atmospheric metallicity priors from JWST and to deep interior architectures. fuzzycore Ariel